Question

Evaluate the expression, correct to six decimal places, by the Change of Base Formula and a calculator

log2^3

Answer 1

\[\Large \log_{2}(3) = \frac{\ln(3)}{\ln(2)}\]


\[\Large \log_{2}(3) \approx \frac{1.098612}{0.693147}\]


\[\Large \log_{2}(3) \approx 1.584962\]

Answer 2

good job jim...you're really helping this precalc noob out

Answer 3

never forget change of base
\[\log_b(x)=\frac{\log_a(x)}{\log_a(b)}\] and since you only have
\[\log_{10}\] and
\[\ln\] on your calculator, those are the ones you can use.
and don't forget what this really tells you. you just solved
\[2^x=3\] for x via
\[x=\frac{\ln(3)}{\ln(2)}\]